Mathematics
Using ruler and compasses only, draw a parallelogram whose diagonals are 4 cm and 6 cm long and contain an angle of 75°. Measure and write down the length of one of the shorter sides of the parallelogram.
Rectilinear Figures
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Answer
Steps of construction:
Let AC = 4 cm and BD = 6 cm.
- Draw AO = produce AO to C such that OC = OA.
- At O construct ∠COP = 75°.
- From OP cut off OD = cm, produce DO to B such that OB = OD.
- Join AB, BC, CD and DA. Then ABCD is the required parallelogram.
On measuring shorter sides, we get
AB = CD = 3.1 cm.
Hence, length of shorter side = 3.1 cm.
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